Optimization of the network structure of a radio communication system

ABSTRACT

Geographically oriented units of a given first hierarchical level of a radio communication system are assigned to geographically oriented units of at least one higher second hierarchical level by: Setting up functions that specify, as a function of a number of subscribers of a radio communication system, a size of a load, that is selected from the group consisting of a radio load and a switching load, and that is caused by a geographically oriented unit of a first hierarchical level at a node of the radio communication system. Setting up a formula which, using the functions, permits a size of a processing load occurring at each node, in a case of a given assignment of geographically oriented units of the first hierarchical level to geographically oriented units of the second hierarchical level, to be calculated for a given number of the subscribers. Using the formula to select an assignment that permits a greatest possible growth in a number of subscribers of the radio communication system without a processing load at a geographically oriented unit of the second hierarchical level exceeding resources of the geographically oriented unit of the second hierarchical level.

BACKGROUND OF THE INVENTION

[0001] Field of the Invention

[0002] The present invention relates to the optimization of the networkstructure of a radio communication system. More precisely, it relates toa method for assigning geographically oriented units of a given firsthierarchical level of a radio communication system to geographicallyoriented units of at least one higher second hierarchical level.

[0003] Radio communication systems such as the GSM system have ahierarchical structure. The lowest level of this structure is formed bytransmitter/receiver stations which communicate by radio with terminals,which in GSM terminology are denoted as base stations, or with the cellsserved by them. A plurality of base stations or their cells are suppliedby a base station controller BSC. The totality of the cells of the basestations supplied by a BSC is therefore also denoted as a BSC region. Aplurality of BSCs are supplied in each case on a higher hierarchicallevel by a mobile switching center (MSC). The totality of the cellsassigned to an MSC is therefore also denoted as the MSC region. Inorder, within an MSC region, to find a subscriber to whom a connectionis to be set up, a search signal is emitted on the broadcast channel andcauses the subscriber terminal to respond. When the number of thesubscribers in an MSC region is low, this search signal can be emittedin all cells of the MSC region. When the number of the subscribers islarge, the capacity of the broadcast channel is not sufficient for thispurpose, and it can be necessary to subdivide this MSC region into aplurality of interconnected location areas and to emit the search signalonly in that location area in which it is known that the targetedsubscriber is located. On the other hand, the subdivision of the MSCregion into location areas will cause the MSC to keep a record as towhich of the various location areas of an MSC region a subscriber iscurrently located in. The processing load which is placed on an MSC bythe management of the mobile subscribers is therefore a function of thetype of division of the MSC region into location areas. The division ofthe MSC region or its location areas into BSC regions also influencesthe processing load. Consequently, there is a need for methods which,starting from a given distribution of base stations, MSCs and BSCs in ageographic zone, in each case permit the specification of assignments ofthe base stations to BSCs, to location areas and/or to MSCs whichminimize the processing load, or permit the largest possible number ofsubscribers to be served for a given processing performance of themobile radio communication system.

[0004] This processing load occurs predominantly in the MSCs. The MSC ina mobile radio communication system has two main functions, callprocessing and mobility management.

[0005] Call processing is understood here as the processing of any typeof voice or data communication. The load caused at the MSC by callprocessing is a function of the type of communication (data, fax, shortmessage service, etc.) and of the position of the two communicatingsubscribers relative to the network topology. It is, for example,different for calls within the mobile radio communication system and forcalls from an external network into the mobile radio communicationsystem or from the mobile radio communication system into an externalnetwork. In the case of calls within a network, as well, the load at theMSC is different depending on whether the two subscribers of a callbelong to the same BSC and/or MSC region or not.

[0006] Mobility management is understood to be all transactions in thesystem which are caused by the tracing and recording in that cell of thenetwork in which an individual subscriber is located. A distinction isto be made here between handover and updating the location of asubscriber (location update).

[0007] Handover is understood as the change of a subscriber from onecell into another cell in simultaneous conjunction with maintaining arunning connection by allocation of resources to the other cell. Theload which is caused by a handover at the MSC depends substantially onthe position of the two cells participating in the handover relative tothe network topology. Three cases which load the MSC to a differentextent in each case, are to be distinguished here:

[0008] a. both cells belong to the same BSC region, but not to the samebase station;

[0009] b. they belong to the same MSC region, but not to the same BSCregion, or

[0010] c. they do not belong to the same MSC region.

[0011] In the case of the GSM network, a handover between cells whichbelong to the same base station need not be taken into account, sincethe MSC does not participate in the management of such a handover.

[0012] A location update takes part when a subscriber changes his cellin the stand-by mode. Two cases are to be distinguished here:

[0013] when the two cells belong to the same location area he need notbe acknowledged by the MSC, nor does he cause a load there, and

[0014] when said subscriber changes the location area (or the MSCregion), this subscriber must be removed from one list in the MSC andentered into another (in the same or another MSC) depending on whetherthe two cells belong to two different location areas within an MSCregion or to two different MSC regions.

[0015] The actual load which is caused at the MSC by these diversemanagement operations, and which can be measured, for example, in theform of required computing time or the number of processor commandsexecuted, can vary for different models of the MSCs.

[0016] However, the optimization of network topologies is complicatednot only by the different types of modes to be taken into account, butalso by virtue of the fact that the individual cells, BSC regions, MSCregions etc., in general terms the various geographically oriented unitsof different hierarchical levels, differ in their properties such as,for example, number of subscribers, subscriber behavior etc.

[0017] All of this renders optimization of a network structure anextremely complex problem to solve which use has been made to dateessentially of empirical rules or heuristic approaches.

SUMMARY OF THE INVENTION

[0018] It is accordingly an object of the invention to provide a methodfor assigning geographically oriented units of a given firsthierarchical level of a radio communication system to geographicallyoriented units of at least one second, higher hierarchical level whichovercomes the above-mentioned disadvantageous of the prior art apparatusand methods of this general type. In particular, it is an object of theinvention to provide such a method that permits effective minimizationof the processing outlay connected with the management of calls andsubscriber mobility, in which the method is based on mathematicalfoundations, and requires a low computational outlay.

[0019] With the foregoing and other objects in view there is provided,in accordance with the invention, a method for assigning geographicallyoriented units of a first hierarchical level of a radio communicationsystem to geographically oriented units of at least one secondhierarchical level that is higher than the first hierarchical level.

[0020] A first step in the method is to set up functions which specify,as a function of the number of subscribers of the radio communicationsystem, the size of a processing load which is caused by ageographically oriented unit of the first hierarchical level at a nodeof the radio communication system such as an MSC for example. A basisfor setting up these functions can be taken from empirical measurementsof the traffic volume and of the subscriber behavior in the individualcells of the radio communication system.

[0021] Starting from these functions, a formula is then set up whichpermits these functions to be used to calculate the processing loadoccurring at the relevant nodes for a given assignment of the units ofthe first hierarchical level to the units of the second hierarchicallevel.

[0022] Using this formula, which supplies the load as a function of thenumber of subscribers in the network, it is possible to select anassignment which permits the greatest possible growth in the number ofsubscribers above the current number of subscribers in the network,without the load to be processed by a node in the radio communicationnetwork exceeding the resources of this node.

[0023] Different methods can be used to select this assignment.

[0024] In accordance with an added feature of the invention, methods oflinear optimization are preferably used to select the assignment. Suchmethods are described in various text books and implemented in amajority of commercially available computer programs.

[0025] In accordance with an additional feature of the invention, themethod can be used on different hierarchical levels of the radiocommunication system. Thus, for example, it is possible to select cellsas units of the first hierarchical level and BSC regions of the radiocommunication system as units of the second hierarchical level, in orderin each case to optimize the structure of the system within the locationarea or MSC region. It is also possible for location areas and/or BSCregions to be taken as units of the second hierarchical level, in orderto optimize the structure of the overall network.

[0026] In accordance with another feature of the invention, in order tokeep the processing simple, the functions which specify the size of theload can be approximated as linear functions of the number ofsubscribers.

[0027] In accordance with a further feature of the invention, asubstantial simplification of the method is provided. This can beachieved by starting from a given, typically actually existingassignment of the units of the first hierarchical level of the radiocommunication system to the units of the second hierarchical level, andwhen selecting the assignment which permits the largest possible rise inthe number of subscribers, by taking account only of assignments whichdiffer from the given assignment only in the case of such units of thefirst hierarchical level as are respectively situated in the givenassignment at the boundaries between two units of the secondhierarchical level. This mode of procedure is particularly expedient inradio communication systems having a large number of units of the firsthierarchical level, since the number of the theoretically possibleassignments of units of the first hierarchical level to the units of thesecond one increases super-exponentially with the number of these units,and the number of assignments possibly to be taken into account isreduced radically in this way.

[0028] Of course, the consequence of such a limitation can be thefailure to find an even better distribution which would have requiredthe redistribution not only of geographically oriented units of thefirst hierarchical level situated at a boundary, but also of a unitadjacent thereto and situated in the interior of a unit of the secondhierarchical level. However, this is not a serious disadvantage since,after a single pass of the method, such a unit of the first hierarchicallevel comes to be situated at the boundary of the newly formed units ofthe second hierarchical level, and can therefore likewise be reorderedby iterative application of the method.

[0029] Other features which are considered as characteristic for theinvention are set forth in the appended claims.

[0030] Although the invention is illustrated and described herein asembodied in an optimization of the network structure of a radiocommunication system, it is nevertheless not intended to be limited tothe details shown, since various modifications and structural changesmay be made therein without departing from the spirit of the inventionand within the scope and range of equivalents of the claims.

[0031] The construction and method of operation of the invention,however, together with additional objects and advantages thereof will bebest understood from the following description of specific embodimentswhen read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0032]FIG. 1 shows an exemplary topology of a radio communication systemto which the method according to the invention can be applied;

[0033]FIG. 2 shows a non-optimized boundary profile betweengeographically oriented units of the radio communication system;

[0034]FIG. 3 shows an optimized boundary profile between the units; and

[0035]FIGS. 4 and 5 illustrate the iterative execution of the method.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0036] Referring now to the figures of the drawing in detail and first,particularly, to FIG. 1 thereof, there is shown an idealizedillustration of the topology of a section of a radio communicationsystem, here a GSM (Global Systems for Mobile Communications) system.Located in the section under consideration are two mobile radioswitching centers MSCk, k=1,2, which are connected in each case to aplurality of base station controllers BSCkl, l=1,2, . . . , illustratedas squares. A plurality of base stations BTSkli, i=1,2, . . . ,illustrated as circles, are connected to each BSC and each supply a cellof the network. The cells, idealized here as hexagons, form a completecoverage of the geographic zone under consideration.

[0037] The cells constitute the geographically oriented units with thelowest hierarchical level in the radio communication system. All cellsconnected to a BSC, for example BSC11, form a BSC region whichconstitutes the geographically oriented unit of the next higherhierarchical level. The BSC regions of BSC11 and BSC12 are combined toform a common location area LA12 which, in turn, forms a geographicallyoriented unit of a higher hierarchical level. The BSC13, likewiseconnected to the MSC1, belongs to another location area LA11, and thisis illustrated in the figure by the bold boundary line L1.

[0038] The two location areas LA11, LA12 together form the MSC regionMSCR1 of the MSC1, which is separated from the MSC region of the MSC2 bya boundary line L2.

[0039] The MSCR2 is not subdivided into location areas.

[0040] It is easy to see that a subscriber who moves within a cell froma point a to b and back does not cause a processing load in the mobilitymanagement of an MSC1 assigned to him. Another subscriber who moves frompoint c to d and over the boundary L1 does, however, cause such a load,because when leaving a location area he has to be removed from the listof the subscribers who can be searched for therein, and entered into anappropriate list of the other location area. Since both location areasbelong to the MSC1, the load occurs completely in the latter. In thecase of a subscriber movement between the points e and f on both sidesof the boundary L2, the load is increased by virtue of the fact that thetwo MSCs between whose regions the subscriber movement takes place mustcommunicate about the entry and removal of the subscriber from therespective lists, in order to ensure that it always remains possible toreach said subscriber.

[0041] The extent of the processing load depends on a multiplicity offactors, naturally for one thing on the number of the subscribers in acell, but also on their mobility behavior and/or communication behavior.The nature and the geographic position of a cell also play a role. Thus,for example, cells located in inner city areas are generallysubstantially smaller than those located in more sparsely populateddistricts, and because of the receiving conditions which vary stronglybecause of buildings, their configuration frequently differs stronglyfrom the idealized hexagon. Consequently, when a subscriber moves in anurban area a multiplicity of cell changes occur even over shortdistances; these changes have to be managed, whereas an equally longmovement outside a town can possibly take place completely within onecell. It is therefore important that the nature of the cells and/or ofthe other geographically oriented units be adapted to the movementbehavior of the subscribers.

[0042]FIG. 2 shows an example of a network topology which is notoptimally adapted. The figure shows a section of a radio communicationnetwork in which three geographic units of identical hierarchical levelA, C, B adjoin one another. A traffic artery D, for example a freeway,comes from the geographic unit A and runs over a short length within theunit C and then returns to the unit A. To simplify the description, itmay be assumed that the geographic units A, C, B are MSC regions, butthe problems are the same with location areas or BSC regions. It isassumed that the subscribers in each of the three regions A, B, Cexhibit the same mobility behavior. Moreover, it may be assumed for thesake of simplicity that the number of subscribers in each of the threeregions is approximately the same. An analysis of the degree of capacityutilization of the MSCs of the regions A, B, C may indicate that theresources of the MSC B are used up by 60%, whereas those of the MSCs Aand C are used up by 80%. At present, all the MSCs can still handle thecommunication traffic without difficulty. However, it must be assumedthat the number of the subscribers will grow in future, and, in allprobability, will do so for all three regions considered atapproximately the same rate. Given the present nature of the regions A,B, C, the MSCs A, B will therefore reach their limit of capacity morequickly than the MSC B, and so investment for extending the capacity inthe regions A, C will become necessary soon, whereas resources willcontinue to lie fallow or unused in the region B. It is thereforedesirable to distribute the processing load as uniformly as possibleover all three regions.

[0043] Since it has been assumed that the number of subscribers and thetraffic model are the same in the various MSC regions, the reasons forthe different resource capacity utilization can be found only in adifferent processing load because of the mobility management in thevarious MSC regions. In the example considered here, these differencescould be ascribed to users who use their mobile telephone when drivingon the freeway D, or keep it on standby, and who thus give rise to anumber of cell changes to be managed which is relatively high withreference to the number of subscribers in the regions A, C.

[0044] In order to reduce this processing load, it would be possible,for example, to separate the part C1 from the region C and add it to theregion A, as shown in FIG. 3, such that the freeway lies completelywithin the region A. However, this would lead to an increase in thenumber of subscribers in the region A at the expense of region C, andwould in this way lead, in turn, to unequal distribution of the load. Inthe simple example considered here of only three regions, the problemcan be solved graphically by a ring exchange in which a subregion B1 isseparated from the region B and added to the region C, and a subregionA1 is separated from the region A and added to the region B such thatthe number of subscribers in all regions once again remainsapproximately equal. The larger the number of the regions to beconsidered in a network, the more difficult it is, however, to find suchsolutions. Moreover, the intuitive finding of a solution mostlypresupposes knowledge of the reasons for an unequal distribution of theload.

[0045] The following approach to the method is therefore proposedaccording to the invention:

[0046] first, a plurality of functions specifying the processing loadwhich is caused by the relevant base station at the assigned MSC aredetermined for each base station of the radio communication system or ofa subregion to be optimized of the radio communication system.

[0047] A first contribution to the processing load of an MSC k comesfrom the call processing of the calls originating from the base station.This load can be different for each base station, and may be given by afunction a_(k,i)(x), i identifying the base station, k the MSC, and xspecifying the number of subscribers. The function, a, can be set up asa function of the number of subscribers of the cell under consideration,but it is simpler for the following consideration when it is formulatedas a function of the total number of the subscribers of the radiocommunication system. It is assumed that the number of the subscribersin a cell can be obtained by multiplying the total number of subscribersby a proportionality factor, the proportionality factor remainingsubstantially unchanged even when the number of the subscribers of theradio communication system grows in the course of time.

[0048] Assuming that S is the total number of subscribers of the radiocommunication system at the present instant, and that g specifies a rateof growth of the number of subscribers in the course of time, the totalload which occurs at a future instant at an arbitrary mobile radioswitching center MSC k can be estimated by the expression$\sum\limits_{i = 1}^{N}{{a_{k,i}\left( {S\left( {1 + g} \right)} \right)}x_{k,i}}$

[0049] the summation index i running over all base stations of the radiocommunication system, and the factor x_(k,i)=1 when the base station iunder consideration belongs to the MSC region k, and is otherwise 0.

[0050] In an analogous way, functions A_(k,l,i,j) can be set up which ineach case specify the load which occurs at the MSC of the base station ibecause of handover and location updates upon the change of a subscriberfrom the cell of the base station i into the cell of a base station jwhen these base stations belong to different MSC regions k, l. The totalload caused within the MSC region k by subscriber change into other MSCregions l can then be written as$\sum\limits_{\underset{l \neq k}{l = 1}}^{M}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{A_{k,l,i,j}\left( {S\left( {1 + g} \right)} \right)}X_{k,l,i,j}}}}$

[0051] where X_(k,l,i,j)=1 when the base station i is located in the MSCregion k and the base station j in the MSC region l, and otherwise being0. Since a handover or location update is possible only between suchbase stations which serve geographically adjacent cells, the summationover the base stations j can be limited to those base stations whichbelong to the set N (i) of the base stations adjacent to the basestation i. M denotes the number of MSC regions.

[0052] Further functions B_(m,n,i,j) are set up for the load which iscaused at the MSC k by location updates and handovers between locationareas within the MSC region k. The total load because of operations ofthis type at the MSC k may be written as$\sum\limits_{m \in {M{(k)}}}{\sum\limits_{\underset{m < n}{n \in {M{(k)}}}}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{B_{m,n,i,j}({pg})}Y_{m,n,i,j}}}}}$

[0053] where Y_(m,n,i,j)=1, when the base station i is located in thelocation area m and the base station j is located in the location arean, and is otherwise 0. Here, as well, the summation can be limited tothose base stations j ∈ N (i) which are adjacent to the base station i,and summation is carried out only over those location areas m, n whichbelong to the set M(k) of the location areas of the MSC k, it beingprohibited for the location areas m, n to be the same.

[0054] A fourth contribution to the processing load is made by handoversand location updates which take place between BSC regions withinindividual location areas. Their contribution may be written as$\sum\limits_{m \in {M{(k)}}}{\sum\limits_{o \in {L{(k)}}}{\sum\limits_{\underset{o < p}{p \in {L{(m)}}}}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{C_{o,p,i,j}\left( {S\left( {1 + g} \right)} \right)}Z_{o,p,i,j}}}}}}$

[0055] C_(o,p,i,j) being a function which specifies the contribution ofthe handovers from the base station i to the base station j on theassumption that i and j belong to different BSC regions o, p of the samelocation area, and Z_(o,p,i,j)=1 when the base station i is situated inthe BSC region o and the base station j is situated in the BSC region p,and is otherwise 0. Once again, the summation extends over all basestations i= . . . , N, over the base station j ∈ N (i) which areadjacent to the base station i, over all location areas m ∈ M (k) whichare situated in the MSC region k, and over all combinations of differentBSC regions o, p from the location area m.

[0056] In order for the radio communication system to be functional, forall of the MSCs, the sum of the four load types must be smaller than thetotal processing capacity L_(k) of the MSC k: $\begin{matrix}{{{{\sum\limits_{i = 1}^{N}{{a_{k,i}\left( {S\left( {1 + g} \right)} \right)}x_{k,i}}} + {\sum\limits_{\underset{l \neq k}{l = 1}}^{M}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{A_{k,l,i,j}\left( {S\left( {1 + g} \right)} \right)}X_{k,l,i,j}}}}} + {\sum\limits_{m \in {M{(k)}}}{\sum\limits_{\underset{m < n}{n \in {M{(k)}}}}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{B_{m,n,i,j}\left( {S\left( {1 + g} \right)} \right)}Y_{m,n,i,j}}}}}} + {\sum\limits_{m \in {M{(k)}}}{\sum\limits_{o \in {L{(k)}}}{\sum\limits_{\underset{o < p}{p \in {L{(m)}}}}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{C_{o,p,i,j}\left( {S\left( {1 + g} \right)} \right)}Z_{o,p,i,j}}}}}}}} \leq L_{k}}\quad {\forall{k \in \left\{ {1,\ldots \quad,M} \right\}}}} & (1)\end{matrix}$

[0057] The network topology or, more accurately, the assignment of thevarious geographically oriented units of the radio communication systemto the geographically oriented units of the next higher hierarchicallevel can be described with the aid of the symbols$x_{k,i} = \left\{ \begin{matrix}1 & {{when}\quad {BTSi}\quad {is}\quad {situated}\quad {in}\quad {the}\quad {MSC}\quad {region}\quad k} \\0 & {otherwise}\end{matrix} \right.$

$y_{m,i} = \left\{ {{\begin{matrix}1 & {{when}\quad {BTSi}\quad {is}\quad {situated}\quad {in}\quad {the}\quad {location}\quad {area}\quad m} \\0 & {otherwise}\end{matrix}z_{o,i}} = \left\{ \begin{matrix}1 & {{when}\quad {BTSi}\quad {is}\quad {situated}\quad {in}\quad {the}\quad {BSC}\quad {region}\quad o} \\0 & {otherwise}\end{matrix} \right.} \right.$

[0058] For these symbols the boundary conditions apply: $\begin{matrix}{{\sum\limits_{k = 1}^{M}x_{k,i}} = 1} & (2) \\{{\sum\limits_{m = 1}y_{m,i}} = x_{k,i}} & (3) \\{{{\sum\limits_{o \in {L{(m)}}}z_{o,i}} = y_{m,i}}{{\forall{i \in \left\{ {1,\ldots \quad,N} \right)}},{\forall{k \in \left\{ {1,{\ldots \quad M}} \right\}}},{\forall{l \in \left\{ {1,\ldots \quad,L} \right\}}}}} & (4)\end{matrix}$

[0059] These formulas correspond to the statement that each base stationBTS i belong more accurately to an MSC region, that it is situated in alocation area which belongs to the same MSC region as the base stationitself, and/or that it is situated in a BSC region which belongs to thesame location area as the base station itself.

[0060] The symbols X, Y, Z can be derived from the symbols x, y, z ineach case by a pair of inequalities:

X _(k,l,i,j)≦min(x _(k,i) ,x _(l,i))  (5)

X _(k,l,i,j) ≧x _(k,i) +x _(l,j)−1  (6)

Y _(m,n,i,j)≦min(y _(m,i) ,y _(n,j))  (7)

Y _(m,n,i,j) ≧y _(m,i) +y _(n,j)−1  (8)

Z _(o,p,i,j)≦min(z _(o,i) ,z _(p,j))  (9)

Z _(o,p,i,j) ≧z _(o,i) ,z _(p,j)−1  (10)

g≦0  (11)

[0061] ∀k,l∈{1, . . . ,M},k≠l,∀m,n∈{1, . . . ,L},m≠n,

[0062] ∀o,p∈{1, . . . ,B},o≠p,∀i∈{1, . . . ,N},∀j∈N(i)

[0063] An optimized distribution of the base stations over the BSCregions, location areas and MSC regions of the radio communicationsystem can now be determined by applying a linear optimization method tothe system of equations and system of inequalities comprising theformulas 1-11. Program systems for this purpose are commerciallyavailable and therefore need not be explained more precisely here. Theprograms lp_solve or Siplex may be mentioned here merely as examples.

[0064] In this model, each base station is assigned to a BSC region, alocation area and an MSC region, but there is no prescription as to theBSCs with which the base stations are connected. The left-hand side ofequation 1 specifies the required resources at the MSC k at the instantt1 when the total number of subscribers has grown from p to pg. Theboundary condition (11) ensures that in the optimization either asolution which permits a positive growth in the number of subscribers,or no solution is found.

[0065] It was assumed in the case of the above approach that a fixedassignment of the location areas to the MSC regions, and of the BSCregions to the location areas is given. This assumption can be weakenedin the following way:

[0066] Once again, assignment of the location areas to the MSC regionsis prescribed, but instead of permanently prescribing each location areathe BSC regions contained therein, the following two sets are defined:

[0067] H(m)=set of all the BSC regions which can be situated in thelocation area m, and

[0068] G(o)=set of all location areas which can contain the BSC regiono,

[0069] and it is required that both sets not be empty. The number oflocation areas and BSC regions is permanently prescribed as in the caseof the previously described model. Instead of the symbols Z_(o,p,i,j)from equation 1, a new symbol W_(m,o,p,i,j) is introduced which is equalto 1 when the base station i belongs to the BSC region o, the basestation j belongs to the BSC region p and the BSC regions k and l belongto the location area m, and is otherwise 0. The following relationshipsare set up using these symbols $\begin{matrix}{{10,000\left( {2 - z_{o,i} - z_{o,j}} \right)} \geq {{\sum\limits_{m \in {G{(o)}}}{l\left( {y_{m,i} - y_{m,j}} \right)}}}} & (12) \\{{\sum\limits_{o = 1}^{B}z_{o,j}} = 1} & (13)\end{matrix}$

$\begin{matrix}{{\sum\limits_{o \in {H{(m)}}}z_{o,i}} \geq y_{m,i}} & (14)\end{matrix}$

W _(m,o,p,i,j)≦min(z _(o,i) ,z _(p,j) ,y _(m,j) y _(m,i))  (15)

W _(m,o,p,i,j) ≧z _(o,i) +z _(p,j) +y _(m,j) +y _(m,i)−3  (16)

[0070] ∀m∈{1, . . . ,L},∀o,p∈{1, . . . ,B},o≠p,∀i∈{1, . . . ,N},∀j∈n(i).

[0071] The formulas 12 to 14 take the place of the formula (4), and theformulas (15) and (16) take the place of (9) and (10), respectively. Theformula (1) is replaced by $\begin{matrix}{{{\sum\limits_{i = 1}^{N}{{a_{k,i}\left( {S\left( {1 + g} \right)} \right)}x_{k,i}}} + {\sum\limits_{\underset{l \neq k}{l = 1}}^{M}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{A_{k,l,i,j}\left( {S\left( {1 + g} \right)} \right)}X_{k,l,i,j}}}}} + {\sum\limits_{m \in {M{(k)}}}{\sum\limits_{\underset{n{\langle m}}{n \in {M{(k)}}}}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{B_{m,n,i,j}\left( {S\left( {1 + g} \right)} \right)}Y_{m,n,i,j}}}}}} + {\sum\limits_{n \in {M{(k)}}}{\sum\limits_{o \in {H{(m)}}}{\sum\limits_{\underset{o{\langle p}}{p \in {H{(m)}}}}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{C_{o,p,i,j}\left( {S\left( {1 + g} \right)} \right)}W_{m,o,p,i,j}}}}}}}} \leq L_{k}} & (17) \\{\forall{k \in \left( {1,\quad \ldots \quad,M} \right\}}} & \quad\end{matrix}$

[0072] The equations (13), (14) ensure that when the base station ibelongs to the location area m it belongs to precisely one BSC region ofrom the set H(m). It holds for this location area m that

m∈G(o) and y _(m,i)=1  (18)

[0073] Because of the large factor 10,000 the formula (12) does notconstitute a limitation when z_(o,i) and z_(o,j) are not both equal to1, that is to say when the base stations i, j do not both belong to theBSC region o. Otherwise, formulas 12 and 18 ensure that the basestations i, j belong to the same location area. In equation (17),summing is carried out over o, p ∈ H (m) instead of over o, p ∈ L(m)because W_(m,o,p,i,j) is equal to 0, when o and p do not both belong tom.

[0074] As mentioned further above, the fixing of location areas leads toan enlargement of the load at the MSC. Consequently, in the case of anoptimization when a complete reordering of all the BSC regions tolocation areas would be allowed, that is to say when the set H(m) wereto contain all BSC regions of the radio communication system and the setG(o) were to contain all location areas, the optimization would lead toall the base stations of an MSC region being allocated to a singlelocation area in order thus to minimize the load which is produced bythe change of subscribers between location areas within an MSC region.Such a result is, however, undesired since, as already explained, itmust lead to overloading of the broadcast channel. It may be excluded bydefining, as an additional boundary condition for the optimization, aminimum ratio 0<q<1 of base stations per MSC region which must beassigned to each location area, that is to say $\begin{matrix}{{{\sum\limits_{i = 1}^{N}y_{m,i}} \geq {q{\sum\limits_{i = 1}^{N}{x_{k,i}\quad {\forall{k \in \left\{ {1,\ldots \quad,M} \right\}}}}}}},{\forall{m \in {M(k)}}},} & (19)\end{matrix}$

[0075] and also taking this boundary condition into account during thelinear optimization.

[0076] Another possibility of generalizing the model is to take intoaccount limitations in capacity for the BSCs or the MSCs. If it isassumed, for example, that there is a limit C for the overall trafficwhich can be managed by a BSC, and that T_(i) is the average trafficgenerated at the base station i, the following boundary condition can beadded to the model $\begin{matrix}{{\sum\limits_{i = 1}^{N}{z_{o,i}T_{i}}} \leq C} & (20)\end{matrix}$

[0077] which holds for each BSC region o. In a similar way, it would bepossible to introduce an upper limit for the size and/or number ofsubscribers of the location areas, in order to limit the load on thebroadcast channel. Other further practical requirements placed on anetwork design can easily be integrated into the model.

[0078] For large numbers of base stations, it is not possible to find anexact solution of the model even by assuming, in order to simplify, thatthe functions a_(k,i)(x), A_(k,l,i,j)(x), B_(m,n,i,j)(x) andC_(o,p,i,j)(x), are linear functions of x.

[0079] In practice, however, the model is frequently not required to beapplied in its entire extent and to the entire network. Consequently,various simplifications are possible. It is possible, for example, tolimit the approach to taking account only of those ones of the varioushandovers and/or location update processes which cause the highestprocessing outlay, generally those which take place between twodifferent MSC regions. This is equivalent to setting the functionsB_(m,n,i,j), C_(o,p,i,j)=0 in formula (1); the optimization task is thensimplified to a problem of selecting the variables X_(k,i) such that theformula $\begin{matrix}{{{{\sum\limits_{i = 1}^{N}{{a_{k,i}\left( {S\left( {1 + g} \right)} \right)}x_{k,i}}} + {\sum\limits_{\underset{l \neq k}{l = 1}}^{M}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{A_{k,l,i,j}\left( {S\left( {1 + g} \right)} \right)}X_{k,l,i,j}}}}}} \leq L_{k}}{\forall{k \in \left\{ {1,\ldots \quad,M} \right\}}}} & (21)\end{matrix}$

[0080] is fulfilled together with the above formulas (2), (5), (6) andthat g reaches a maximum. When the functions a_(k,i)(x) andA_(k,l,i,j)(x) can be approximated by linear functions in the form ofa_(k,i)(S(1+g))=(1+g) a_(k,i)(S), the formula 21 can also be written as$\begin{matrix}{{{\left( {1 + h} \right)\quad \left( {{\sum\limits_{i = 1}^{N}{{a_{i}(p)}x_{k,i}}} + {\sum\limits_{\underset{l \neq k}{l = 1}}^{M}{\sum\limits_{i = 1}^{N}{\sum\limits_{j \in {N{(i)}}}{{A_{i,j}(p)}X_{k,l,i,j}}}}}} \right)} \leq {hL}_{k}}\quad {\forall{k \in \left\{ {1,\ldots \quad,M} \right\}}}} & \left( 21^{\prime} \right)\end{matrix}$

[0081] where h=1/g. The optimization task is then to select the x_(k,i)such that h can be selected as small as possible.

[0082] In general, a network planner will not attempt to redesign theentire structure of the network from scratch, but he will only optimizethe regions at the boundaries of the MSC regions. FIG. 4 illustratesthis with the aid of the same network section which has already beenillustrated in FIG. 1. Those cells of the MSC regions MSCR1 and MSCR2which are not adjacent to the respective other region are emphasized byhatching. The assignment of these cells to their MSC regions is not tobe called into question in the optimization; the contributions of thesecells to the processing load can therefore be summarized in theoptimization to the constant term σ and the summation is performed notover all base stations i=1, . . . N, but only over those base stations iwhich are situated at the boundary of the MSC regions. $\begin{matrix}{{{\left( {1 + h} \right)\quad \left( {{\sum\limits_{i = 1}^{N}{{a_{k,i}(p)}x_{k,i}}} + {\sum\limits_{\underset{l \neq k}{l = 1}}^{M}{\sum\limits_{i}{\sum\limits_{j \in {N{(i)}}}{{A_{k,l,i,j}(p)}X_{k,l,i,j}}}}}} \right)} \leq {h\left( {L_{k} - \sigma} \right)}}\quad {\forall{k \in \left\{ {1,\ldots \quad,M} \right\}}}} & (22)\end{matrix}$

0<h<∞

[0083] A possible result of this optimization is illustrated in FIG. 5:two base stations BTS211, BTS212, which were still assigned to the BSC21in FIG. 4, have been added to the BSC11. Consequently, the position ofthe boundary line L2 between the two MSC regions is displaced, and theset of the base stations to be taken into account in a secondoptimization step is changed.

[0084] When the optimization for the new boundary line L2′ is repeated,it is then also possible to bring into question the assignment of basestations to the MSC region MSCR2 which were not yet situated at theboundary in the state shown in FIG. 4, such as the base stations BTS213,BTS221, for example. It is therefore possible by multiple repetition ofan optimization limited to the boundary region also to optimize deepreaching changes in the network structure with a low outlay incomputation.

[0085] The above description took account only of the optimization ofthe assignment of base stations or of the cells supplied by them togeographically oriented units of a higher hierarchical level of thenetwork. However, it is evident that a corresponding optimization canalso be carried out for the assignment of BSC regions to location areasor MSC regions when load functions such as the functions a_(i), A_(i,j)etc. are formulated for entire MSC regions instead of for the basestations, and these functions are used to set up a formula which permitscalculation of the resulting load at the MSCs for given assignments ofBSCs to location areas and MSCs.

I claim:
 1. A method for assigning geographically oriented units of afirst hierarchical level of a radio communication system togeographically oriented units of at least one second hierarchical levelthat is higher than the first hierarchical level, which comprises:setting up functions that specify, as a function of a number ofsubscribers of a radio communication system, a size of a load, that isselected from the group consisting of a radio load and a switching load,and that is caused by a geographically oriented unit of a firsthierarchical level at a node of the radio communication system; settingup a formula which, using the functions, permits a size of a processingload occurring at each node, in a case of a given assignment ofgeographically oriented units of the first hierarchical level togeographically oriented units of the second hierarchical level, to becalculated for a given number of the subscribers; and using the formulato select an assignment that permits a greatest possible growth in anumber of subscribers of the radio communication system without aprocessing load at a geographically oriented unit of the secondhierarchical level exceeding resources of the geographically orientedunit of the second hierarchical level.
 2. The method according to claim1 , which comprises using a method of linear optimization to select theassignment.
 3. The method according to claim 1 , wherein: thegeographically oriented units of the first hierarchical level are unitsselected from the group consisting of cells of the radio communicationsystem and base stations of the radio communication system; and thegeographically oriented units of the second hierarchical level are unitsselected from the group consisting of mobile switching center regions,location areas, and base station controller regions.
 4. The methodaccording to claim 1 , which comprises approximating the functions usinglinear functions of the number of subscribers.
 5. The method accordingto claim 1 , which comprises: using an existing assignment of thegeographically oriented units of the first hierarchical structure of theradio communication system to the geographically oriented units of thesecond hierarchical structure as a starting point; and considering onlygeographically oriented units of the first hierarchical structure whichare situated at a boundary between two geographically oriented units ofthe second hierarchical structure.
 6. The method according to claim 5 ,which comprises using iteration.